Harry:

"Patrick Reany" wrote in message
. com...

The group property of the Lorentz transformation suggests strongly
otherwise.

Not surprising: the group property was designed to comply to the PoR.

Be serious. The so-called "group property" is a mathematical concept
that existed before physicists had any idea it was useful. The group
property for a set of objects A,B,... upon which a rule for composition
is defined, satisfies the following properties:

(1) If A and B are members of the group, then C = AB is a member of
the group.

(2) There exists an inverse such that AA^-1 = 1, for all A.

(3) There is an identity, I, so that AI = A, for all A,

(4) The composition is associative: (AB)C = A(BC)

Physicists did, however rapidly come to appreciate the physics
that can be extracted from the symmetry which group theory makes
apparent - like deriving conservation laws instead of assuming
them.

For continuous groups such as lie groups, (rotations in a plane,
lorentz boosts, etc.), you have a very simple structure. Everything
about the group is determined by examining the infinitessimal trans-
formation in the neighborhood of the identity.

(Bilge) wrote in message ...
Harry:

"Patrick Reany" wrote in message
. com...

The group property of the Lorentz transformation suggests strongly
otherwise.

Not surprising: the group property was designed to comply to the PoR.

Be serious. The so-called "group property" is a mathematical concept
that existed before physicists had any idea it was useful. The group
property for a set of objects A,B,... upon which a rule for composition
is defined, satisfies the following properties:

(1) If A and B are members of the group, then C = AB is a member of
the group.

(2) There exists an inverse such that AA^-1 = 1, for all A.

(3) There is an identity, I, so that AI = A, for all A,

(4) The composition is associative: (AB)C = A(BC)

Physicists did, however rapidly come to appreciate the physics
that can be extracted from the symmetry which group theory makes
apparent - like deriving conservation laws instead of assuming
them.

For continuous groups such as lie groups, (rotations in a plane,
lorentz boosts, etc.), you have a very simple structure. Everything
about the group is determined by examining the infinitessimal trans-
formation in the neighborhood of the identity.

Sorry, sometimes I omit dscriptive words that I think are understood.
Thanks anyway for the precision!

I meant that the Lorentz transformations were designed with in order
to comply with the PoR. In fact it happened in two steps: first
intuitively by Lorentz, and it seems not free of error, and then
corrected and rewritten by Poincare - who emphasised their group
properties - in the symmetric form that we use today.

Harald

"Harry" wrote in message
om...
(Bilge) wrote in message
...
Harry:

"Patrick Reany" wrote in message
. com...

The group property of the Lorentz transformation suggests strongly
otherwise.

Not surprising: the group property was designed to comply to the PoR.

Be serious. The so-called "group property" is a mathematical concept
that existed before physicists had any idea it was useful. The group
property for a set of objects A,B,... upon which a rule for composition
is defined, satisfies the following properties:

(1) If A and B are members of the group, then C = AB is a member of
the group.

(2) There exists an inverse such that AA^-1 = 1, for all A.

(3) There is an identity, I, so that AI = A, for all A,

(4) The composition is associative: (AB)C = A(BC)

Physicists did, however rapidly come to appreciate the physics
that can be extracted from the symmetry which group theory makes
apparent - like deriving conservation laws instead of assuming
them.

For continuous groups such as lie groups, (rotations in a plane,
lorentz boosts, etc.), you have a very simple structure. Everything
about the group is determined by examining the infinitessimal trans-
formation in the neighborhood of the identity.

Sorry, sometimes I omit dscriptive words that I think are understood.
Thanks anyway for the precision!

I meant that the Lorentz transformations were designed with in order
to comply with the PoR. In fact it happened in two steps: first
intuitively by Lorentz, and it seems not free of error, and then
corrected and rewritten by Poincare - who emphasised their group
properties - in the symmetric form that we use today.

Harald
The meaning of PoR is vague. Before Einstein it meant the vector addition of
velocities, most simply expressed as V=u+v, omitting any angle. But after
Einstein we have the composition of velocities, which includes c into the
equation, making it
V = (u+v)/(1+uv/c^2).
Clearly these are different PoRs, they have different equations.
Einstein was compelled to introduce a new postulate as his first, but
disguised it, not disclosing it until later, to introduce his second
postulate.
Hence his equation
1/2[tau(0,0,0,t)+tau(0,0,0,t+x'/(c-v)+x'/(c+v))] = tau(x',0,0,t+x'/(c-v))
is incorrect.
The term x'/(c+v) should use the composition of velocities, not the vector
addition of velocities, otherwise he is using the wrong PoR. Any velocity
composition with c has c as the result.
c (group operator) v = c.

This must then obviously reduce to
1/2[tau(0,0,0,t)+tau(0,0,0,t+2x'/c)] = tau(x',0,0,t+x'/c)
and tau = t.
Not a very interesting conclusion, perhaps, but there it is.
Clearly his argument is invalid, he isn't consistent.

Androcles

"Androcles" wrote in message
...

"Harry" wrote in message
om...
SNIP

I meant that the Lorentz transformations were designed with in order
to comply with the PoR. In fact it happened in two steps: first
intuitively by Lorentz, and it seems not free of error, and then
corrected and rewritten by Poincare - who emphasised their group
properties - in the symmetric form that we use today.

Harald

The meaning of PoR is vague. Before Einstein it meant the vector addition
of
velocities, most simply expressed as V=u+v, omitting any angle.

No, not anymore with Poincare's Principle of Relativity (from ca. 1900), and
certainly not after the theory of Lorentz...

But after
Einstein we have the composition of velocities, which includes c into the
equation, making it
V = (u+v)/(1+uv/c^2).
Clearly these are different PoRs, they have different equations.

Mathematically there is nothing different about the PoR's of Poincare and
Einstein.

Einstein was compelled to introduce a new postulate as his first, but
disguised it, not disclosing it until later, to introduce his second
postulate.
Hence his equation
1/2[tau(0,0,0,t)+tau(0,0,0,t+x'/(c-v)+x'/(c+v))] = tau(x',0,0,t+x'/(c-v))
is incorrect.
The term x'/(c+v) should use the composition of velocities, not the vector
addition of velocities, otherwise he is using the wrong PoR. Any velocity
composition with c has c as the result.
c (group operator) v = c.

I think you misunderstand how to correctly use the velocity addition
formula:
It applies to the addition of the speed of something as measured in a moving
system by a stationary system.
Here we have only the speed of something relative to a light beam. The
measured speed of light relative to that system is c.
According to that equation, the measured speed of light relative to your
system is also c.
But that does not change that according to your measurements, the relative
speed between that system and the light is c+v.

Harald

Androcles wrote:

"Harry" wrote in message
om...

(Bilge) wrote in message

...

Harry:

"Patrick Reany" wrote in message
. com...

The group property of the Lorentz transformation suggests strongly
otherwise.

Not surprising: the group property was designed to comply to the PoR.

Be serious. The so-called "group property" is a mathematical concept
that existed before physicists had any idea it was useful. The group
property for a set of objects A,B,... upon which a rule for composition
is defined, satisfies the following properties:

(1) If A and B are members of the group, then C = AB is a member of
the group.

(2) There exists an inverse such that AA^-1 = 1, for all A.

(3) There is an identity, I, so that AI = A, for all A,

(4) The composition is associative: (AB)C = A(BC)

Physicists did, however rapidly come to appreciate the physics
that can be extracted from the symmetry which group theory makes
apparent - like deriving conservation laws instead of assuming
them.

For continuous groups such as lie groups, (rotations in a plane,
lorentz boosts, etc.), you have a very simple structure. Everything
about the group is determined by examining the infinitessimal trans-
formation in the neighborhood of the identity.

Sorry, sometimes I omit dscriptive words that I think are understood.
Thanks anyway for the precision!

I meant that the Lorentz transformations were designed with in order
to comply with the PoR. In fact it happened in two steps: first
intuitively by Lorentz, and it seems not free of error, and then
corrected and rewritten by Poincare - who emphasised their group
properties - in the symmetric form that we use today.

Harald

The meaning of PoR is vague. Before Einstein it meant the vector addition of
velocities, most simply expressed as V=u+v, omitting any angle.
That is not true. You are equating the PoR with a consequence of the
PoR that depends on the additional assumption of absolute time.

...But after
Einstein we have the composition of velocities, which includes c into the
equation, making it
V = (u+v)/(1+uv/c^2).
Same error, but this time you confuse the PoR with a consequence of the
PoR that depends on the existence of a finite invariant velocity.

Clearly these are different PoRs, they have different equations.
GIGO.
Einstein was compelled to introduce a new postulate as his first, but
disguised it, not disclosing it until later, to introduce his second
postulate.
Hence his equation
1/2[tau(0,0,0,t)+tau(0,0,0,t+x'/(c-v)+x'/(c+v))] = tau(x',0,0,t+x'/(c-v))
is incorrect.
The term x'/(c+v) should use the composition of velocities, not the vector
addition of velocities, otherwise he is using the wrong PoR.
No, relative velocity is correctly calculated using the vector law
between velocities in the same inertial system. It is only when
transforming velocity between inertial systems that the composition law
is required.

..Any velocity
composition with c has c as the result.
c (group operator) v = c.

This must then obviously reduce to
1/2[tau(0,0,0,t)+tau(0,0,0,t+2x'/c)] = tau(x',0,0,t+x'/c)
and tau = t.
Not a very interesting conclusion, perhaps, but there it is.
Clearly his argument is invalid, he isn't consistent.

GIGO



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"Harry" wrote in message
...

"Androcles" wrote in message
...

"Harry" wrote in message
om...
SNIP

I meant that the Lorentz transformations were designed with in order
to comply with the PoR. In fact it happened in two steps: first
intuitively by Lorentz, and it seems not free of error, and then
corrected and rewritten by Poincare - who emphasised their group
properties - in the symmetric form that we use today.

Harald

The meaning of PoR is vague. Before Einstein it meant the vector
addition
of
velocities, most simply expressed as V=u+v, omitting any angle.

No, not anymore with Poincare's Principle of Relativity (from ca. 1900),
and
certainly not after the theory of Lorentz...
Amazed...
Ok, before Poincare is was different. What the heck! It's still different!

But after
Einstein we have the composition of velocities, which includes c into
the
equation, making it
V = (u+v)/(1+uv/c^2).
Clearly these are different PoRs, they have different equations.

Mathematically there is nothing different about the PoR's of Poincare and
Einstein.
But there is a hell of a difference between the PoR of Poincare and Galileo!


Einstein was compelled to introduce a new postulate as his first, but
disguised it, not disclosing it until later, to introduce his second
postulate.
Hence his equation
1/2[tau(0,0,0,t)+tau(0,0,0,t+x'/(c-v)+x'/(c+v))] =
tau(x',0,0,t+x'/(c-v))
is incorrect.
The term x'/(c+v) should use the composition of velocities, not the
vector
addition of velocities, otherwise he is using the wrong PoR. Any
velocity
composition with c has c as the result.
c (group operator) v = c.

I think you misunderstand how to correctly use the velocity addition
formula:

Too right I do!
Seems to me that you can try to use the Galilean PoR when it suits you and
the
Poincare PoR when that suits in a desperate attempt to prop up your absurd
pet theory under any circumstances.

It applies to the addition of the speed of something as measured in a
moving
system by a stationary system.

Really? Is that the Poincare or the Galileo version?
How are we supposed to know the difference?
I think you misunderstand how to correctly apply logic.

Here we have only the speed of something relative to a light beam. The
measured speed of light relative to that system is c.
Measured? By whom? When was it measured? I'm calling you on it. You are
bluffing, you are making it up. In short, you are telling a deliberate lie.
Einstein never claimed it was measured, so why do you?
Now back up your ridiculous claim with some facts.
I think you misunderstand how to correctly lie convincingly.
I think that you are a liar.
Androcles

Androcles wrote:

"Harry" wrote in message
om...

(Bilge) wrote in message

...

Harry:

"Patrick Reany" wrote in message
. com...

The group property of the Lorentz transformation suggests strongly
otherwise.

Not surprising: the group property was designed to comply to the PoR.

Be serious. The so-called "group property" is a mathematical concept
that existed before physicists had any idea it was useful. The group
property for a set of objects A,B,... upon which a rule for composition
is defined, satisfies the following properties:

(1) If A and B are members of the group, then C = AB is a member of
the group.

(2) There exists an inverse such that AA^-1 = 1, for all A.

(3) There is an identity, I, so that AI = A, for all A,

(4) The composition is associative: (AB)C = A(BC)

Physicists did, however rapidly come to appreciate the physics
that can be extracted from the symmetry which group theory makes
apparent - like deriving conservation laws instead of assuming
them.

For continuous groups such as lie groups, (rotations in a plane,
lorentz boosts, etc.), you have a very simple structure. Everything
about the group is determined by examining the infinitessimal trans-
formation in the neighborhood of the identity.

Sorry, sometimes I omit dscriptive words that I think are understood.
Thanks anyway for the precision!

I meant that the Lorentz transformations were designed with in order
to comply with the PoR. In fact it happened in two steps: first
intuitively by Lorentz, and it seems not free of error, and then
corrected and rewritten by Poincare - who emphasised their group
properties - in the symmetric form that we use today.

Harald

The meaning of PoR is vague. Before Einstein it meant the vector addition of
velocities, most simply expressed as V=u+v, omitting any angle. But after
Einstein we have the composition of velocities, which includes c into the
equation, making it
V = (u+v)/(1+uv/c^2).
Clearly these are different PoRs, they have different equations.
Einstein was compelled to introduce a new postulate as his first, but
disguised it, not disclosing it until later, to introduce his second
postulate.
Let me reverse your argument:

The speed of light does not obey the V=u+v law, so, if you are right,
then the "old" PoR does not apply to optics. Either the PoR is
restricted to mechanics, or it must be rejected.

We are left with the interesting case that the results of optical
experiments are not sensitive to absolute velocity, but the PoR does not
apply precisely because of the explanation of that failure.

Einstein saw that the way out of the dilemma was to include optics (and
EM) in the PoR, and modify our ideas about time.



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"Brian Kennelly" wrote in message
...
Androcles wrote:

"Harry" wrote in message
om...

(Bilge) wrote in message

...

Harry:

"Patrick Reany" wrote in message
. com...

The group property of the Lorentz transformation suggests strongly
otherwise.

Not surprising: the group property was designed to comply to the PoR.

Be serious. The so-called "group property" is a mathematical concept
that existed before physicists had any idea it was useful. The group
property for a set of objects A,B,... upon which a rule for composition
is defined, satisfies the following properties:

(1) If A and B are members of the group, then C = AB is a member of
the group.

(2) There exists an inverse such that AA^-1 = 1, for all A.

(3) There is an identity, I, so that AI = A, for all A,

(4) The composition is associative: (AB)C = A(BC)

Physicists did, however rapidly come to appreciate the physics
that can be extracted from the symmetry which group theory makes
apparent - like deriving conservation laws instead of assuming
them.

For continuous groups such as lie groups, (rotations in a plane,
lorentz boosts, etc.), you have a very simple structure. Everything
about the group is determined by examining the infinitessimal trans-
formation in the neighborhood of the identity.

Sorry, sometimes I omit dscriptive words that I think are understood.
Thanks anyway for the precision!

I meant that the Lorentz transformations were designed with in order
to comply with the PoR. In fact it happened in two steps: first
intuitively by Lorentz, and it seems not free of error, and then
corrected and rewritten by Poincare - who emphasised their group
properties - in the symmetric form that we use today.

Harald

The meaning of PoR is vague. Before Einstein it meant the vector
addition of
velocities, most simply expressed as V=u+v, omitting any angle.

That is not true.
Yes it is true.

You are equating the PoR with a consequence of the
PoR that depends on the additional assumption of absolute time.

Exactly. Well done.
Einstein has used the concept of absolute time to compute
x'/(c+v), where he should have used relative time and the PoR to compute
x'/(c+v)/(1+vc/c^2) =
x'/(c+v)/(1+v/c) =
x'.(1+v/c)/(c+v) =
x'.(c/c+v/c)/(c+v) =
x'.((c+v)/c)/(c+v) =
x'/c


...But after
Einstein we have the composition of velocities, which includes c into
the
equation, making it
V = (u+v)/(1+uv/c^2).
Same error, but this time you confuse the PoR with a consequence of the
PoR that depends on the existence of a finite invariant velocity.

Clearly these are different PoRs, they have different equations.
GIGO.
Exactly. Well done. Relativity is garbage.

Einstein was compelled to introduce a new postulate as his first, but
disguised it, not disclosing it until later, to introduce his second
postulate.
Hence his equation
1/2[tau(0,0,0,t)+tau(0,0,0,t+x'/(c-v)+x'/(c+v))] =
tau(x',0,0,t+x'/(c-v))
is incorrect.
The term x'/(c+v) should use the composition of velocities, not the
vector
addition of velocities, otherwise he is using the wrong PoR.
No, relative velocity is correctly calculated using the vector law
between velocities in the same inertial system.
ROFLMAO!
Velocities in the same inertial system!
Stop it, my sides are splitting!
After all the explaining about the "greek" frame and the "latin" frame from
Paul Andersen, or the "stationary" frame and the "moving" frame from
Einstein, you come up with a howler like that!


It is only when
transforming velocity between inertial systems that the composition law
is required.
Yeah, right, ok! LOL... so the REAL velocity of light is c+v, and it takes
the REAL time of x'/(c+v) to travel a distance x'.


..Any velocity
composition with c has c as the result.
c (group operator) v = c.

This must then obviously reduce to
1/2[tau(0,0,0,t)+tau(0,0,0,t+2x'/c)] = tau(x',0,0,t+x'/c)
and tau = t.
Not a very interesting conclusion, perhaps, but there it is.
Clearly his argument is invalid, he isn't consistent.

GIGO

Exactly right. If you being with the garbage "light is always propagated in
empty space with a definite velocity c which is independent of the state of
motion of the emitting body", then you are bound to get garbage for a
result.
What happens when two contra-revolving satellites pass each other? Each see
the other's clock as running slow, right? But when they meet again, they
have exactly the same time! Amazing. What a tremendous conclusion! They pass
each other 4 times,
twice when on the same side of the Earth and twice when they are on opposite
sides, and always each sees the other's clock running slow and telling the
right time. When did they see the other's clock speed up again? DUH!
Time is absolute, proven by reductio-ad-absurdum. Einstein's relativity is
garbage.
QED.

Androcles wrote:
"Brian Kennelly" wrote in message
...

Androcles wrote:


"Harry" wrote in message
e.com...


(Bilge) wrote in message

que-al.net...


Harry:

"Patrick Reany" wrote in message
ogle.com...

The group property of the Lorentz transformation suggests strongly
otherwise.

Not surprising: the group property was designed to comply to the PoR.

Be serious. The so-called "group property" is a mathematical concept
that existed before physicists had any idea it was useful. The group
property for a set of objects A,B,... upon which a rule for composition
is defined, satisfies the following properties:

(1) If A and B are members of the group, then C = AB is a member of
the group.

(2) There exists an inverse such that AA^-1 = 1, for all A.

(3) There is an identity, I, so that AI = A, for all A,

(4) The composition is associative: (AB)C = A(BC)

Physicists did, however rapidly come to appreciate the physics
that can be extracted from the symmetry which group theory makes
apparent - like deriving conservation laws instead of assuming
them.

For continuous groups such as lie groups, (rotations in a plane,
lorentz boosts, etc.), you have a very simple structure. Everything
about the group is determined by examining the infinitessimal trans-
formation in the neighborhood of the identity.

Sorry, sometimes I omit dscriptive words that I think are understood.
Thanks anyway for the precision!

I meant that the Lorentz transformations were designed with in order
to comply with the PoR. In fact it happened in two steps: first
intuitively by Lorentz, and it seems not free of error, and then
corrected and rewritten by Poincare - who emphasised their group
properties - in the symmetric form that we use today.

Harald

The meaning of PoR is vague. Before Einstein it meant the vector

addition of

velocities, most simply expressed as V=u+v, omitting any angle.

That is not true.

Yes it is true.


You are equating the PoR with a consequence of the
PoR that depends on the additional assumption of absolute time.


Exactly. Well done.
So why do you continue to post this stuff?

Einstein was compelled to introduce a new postulate as his first, but
disguised it, not disclosing it until later, to introduce his second
postulate.
Hence his equation
1/2[tau(0,0,0,t)+tau(0,0,0,t+x'/(c-v)+x'/(c+v))] =

tau(x',0,0,t+x'/(c-v))

is incorrect.
The term x'/(c+v) should use the composition of velocities, not the

vector

addition of velocities, otherwise he is using the wrong PoR.

No, relative velocity is correctly calculated using the vector law
between velocities in the same inertial system.

ROFLMAO!
Velocities in the same inertial system!
Stop it, my sides are splitting!
After all the explaining about the "greek" frame and the "latin" frame from
Paul Andersen, or the "stationary" frame and the "moving" frame from
Einstein, you come up with a howler like that!

Please explain what you consider to be a howler. Velocity is rate of
change of position with time. Relative velocities are calculated by
dividing the change of displacement by the time of the change. In a
single inertial system, the denominator is a simple scalar and the
vector law results.



It is only when
transforming velocity between inertial systems that the composition law
is required.

Yeah, right, ok! LOL... so the REAL velocity of light is c+v, and it takes
the REAL time of x'/(c+v) to travel a distance x'.

The relative velocity between light with velocity 'c' and a fixed point
moving at velocity '-v' is 'c+v', so yes, if x' describes the length of
a rod moving in the opposite direction of a light signal, then the time
of travel is x'/(c+v). It is easy to prove.

What happens when two contra-revolving satellites pass each other? Each see
the other's clock as running slow, right? But when they meet again, they
have exactly the same time! Amazing. What a tremendous conclusion! They pass
each other 4 times,
twice when on the same side of the Earth and twice when they are on opposite
sides, and always each sees the other's clock running slow and telling the
right time. When did they see the other's clock speed up again? DUH!
The satellites are not inertial systems, so you must take the
acceleration into account. I have not done the math, but the change due
to the equivalence principle will probably show the correct speedup when
the satellites are on opposite sides of the Earth. Try it.

Time is absolute, proven by reductio-ad-absurdum.
Not yet. You have done an incomplete analysis.



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Androcles wrote:

"Brian Kennelly" wrote in message
...

Androcles wrote:


"Harry" wrote in message
e.com...


(Bilge) wrote in message

que-al.net...


Harry:

"Patrick Reany" wrote in message
ogle.com...

The group property of the Lorentz transformation suggests strongly
otherwise.

Not surprising: the group property was designed to comply to the PoR.

Be serious. The so-called "group property" is a mathematical concept
that existed before physicists had any idea it was useful. The group
property for a set of objects A,B,... upon which a rule for composition
is defined, satisfies the following properties:

(1) If A and B are members of the group, then C = AB is a member of
the group.

(2) There exists an inverse such that AA^-1 = 1, for all A.

(3) There is an identity, I, so that AI = A, for all A,

(4) The composition is associative: (AB)C = A(BC)

Physicists did, however rapidly come to appreciate the physics
that can be extracted from the symmetry which group theory makes
apparent - like deriving conservation laws instead of assuming
them.

For continuous groups such as lie groups, (rotations in a plane,
lorentz boosts, etc.), you have a very simple structure. Everything
about the group is determined by examining the infinitessimal trans-
formation in the neighborhood of the identity.

Sorry, sometimes I omit dscriptive words that I think are understood.
Thanks anyway for the precision!

I meant that the Lorentz transformations were designed with in order
to comply with the PoR. In fact it happened in two steps: first
intuitively by Lorentz, and it seems not free of error, and then
corrected and rewritten by Poincare - who emphasised their group
properties - in the symmetric form that we use today.

Harald

The meaning of PoR is vague. Before Einstein it meant the vector

addition of

velocities, most simply expressed as V=u+v, omitting any angle. But

after

Einstein we have the composition of velocities, which includes c into

the

equation, making it
V = (u+v)/(1+uv/c^2).
Clearly these are different PoRs, they have different equations.
Einstein was compelled to introduce a new postulate as his first, but
disguised it, not disclosing it until later, to introduce his second
postulate.

Let me reverse your argument:

The speed of light does not obey the V=u+v law,

Evidence, please.
Fresnel's hypothesis, which has been experimentally verified, says that
light speed transforms as V=c/N+v(1-1/N^2). This is in obvious conflict
with V=c/N+v.


..Einstein equation,
1/2[tau(0,0,0,t)+tau(0,0,0,t+x'/(c-v)+x'/(c+v))] = tau(x',0,0,t+x'/(c-v))
Reference :
http://www.fourmilab.ch/etexts/einstein/specrel/www/
says it does.

Actually, Einstein goes on from that equation to show that no velocities
obey the V=u+v law when changing reference systems.



so, if you are right,
then the "old" PoR does not apply to optics.

Evidence, please. I accept no assertions. The old PoR applies to optics, see
the above, and see the attachment.
If the PoR is equivalent to, or requires, V=u+v, then Fresnel's formula
shows that light does not conform to the PoR.

Your attachment is not an application of the PoR.




Either the PoR is
restricted to mechanics, or it must be rejected.

See the above.


We are left with the interesting case that the results of optical
experiments are not sensitive to absolute velocity,

Keep going...


but the PoR does not
apply precisely because of the explanation of that failure.

Very good. What failure?
The failure to detect any dependence on absolute velocity.
IOW, experimentally, optics obeys the PoR, but theoretically it does not
(using your definition of the PoR). Fresnel's hypothesis explains the
failure to detect absolute velocity but it violates your definition of
the PoR.




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